KR100454342B1 - Velocity profile producing method for industrial robot - Google Patents

Abstract

The present invention relates to a method for generating a speed profile of an industrial robot. According to the present invention, a velocity profile generation method includes calculating time variables of acceleration / deceleration time and constant velocity time based on a given speed, acceleration, and movement distance, and calculating the calculated time variables using the following equation,

(t _i 'is the normalized time variable, t _i is the time variable before normalization, ROUND represents the rounding operator, and RST represents the sampling time, respectively). Calculating speed and acceleration in each exercise section using the calculated time variables. According to the present invention, by normalizing the time variables calculated in the velocity profile generation process during the joint motion of the robot to an integer multiple of the sampling time (RST) and recalculating the velocity and acceleration using the same, the position error occurs at the end point. Can be prevented.

Description

Velocity profile producing method for industrial robot

The present invention relates to a speed profile generation method for acceleration / deceleration control of an industrial robot, and more particularly, to generate a speed profile that can minimize vibration during robot motion by normalizing acceleration, deceleration, and constant velocity times to an integer multiple of the sampling time. It is about a method.

In general, an industrial articulated robot moves an end effector to a target position by rotating each joint, and thus, a servo motor is provided for each joint as a driving source for rotating each joint. The reliability and durability of high-speed and high-precision robots depends on how much the noise and vibration generated by each joint axis of the robot can be reduced. Therefore, in generating the velocity profile for controlling the servomotor of the articulated robot, it is important to smoothly move each joint and reduce the operation time.

As shown in FIG. 1, when the movement trajectory of the robot is configured to stop at the end point C from the start point A past the waypoint B, the robot does not stop but gently passes the waypoint B. It is called continuous motion. In order to realize such continuous motion, when the movement amount, speed, and acceleration for each movement section are given, the control device of the robot calculates the acceleration / deceleration time, the constant velocity time, the constant velocity, and the like to generate a velocity profile to accelerate and decelerate each joint. To control the movement.

Various examples of the conventional speed profile generation method are disclosed in Patent Publication No. 0157454, Patent Publication No. 0183657, and Patent Publication No. 2001-3878.

By the way, according to the conventional speed profile generation method disclosed in the above publications, the control device of the robot calculates the movement amount of each joint at every sampling time, since the acceleration and deceleration time and the constant speed are not normalized, so that the constant velocity and the acceleration and deceleration are Position data is calculated discontinuously at the inflection point of the rapid motion or when decelerating and stopping. Therefore, there is a problem that vibration and position error are generated due to the unprocessed position data in the previous movement step.

The present invention has been made to solve the above problems, and when each joint of the robot is a continuous movement, the acceleration and deceleration time and the constant speed time by normalizing the position update time, that is, the sampling time in the control device An object of the present invention is to provide a speed profile generation method that can reduce vibrations caused by position errors in an exercise step.

1 is a view showing an example of the movement trajectory during the continuous movement of the robot.

Figure 2 is a graph showing an example of the speed profile during continuous motion as shown in FIG.

3 is a graph showing a moving distance not reached when generating an acceleration time before and after the waypoint of FIG.

The object of the present invention as described above is (a) calculating time variables of acceleration and deceleration time and constant velocity time based on a given speed, acceleration and moving distance, and (b) normalizing the time variables to an integer multiple of the sampling time. And (c) calculating velocity and acceleration in each movement section using the normalized time variables.

Here, the normalization of the time variables in step (b) is the following equation,

(t _i 'denotes a normalized time variable, t _i denotes a time variable before normalization, ROUND denotes a rounding operator, and RST denotes a sampling time.)

Further, in the step (c) the speed is the following equation,

(V ₁ 'is the constant velocity, t _d12 ' is the normalized total travel time, and t ₁ 'is the normalized acceleration time, respectively.)

On the other hand, the velocity profile generation method of the present invention may further comprise the step of calculating the movement amount for each sampling time using the calculation results in the step (b) and (c).

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the present invention.

When the robot moves along a motion trajectory as shown in FIG. 1, one particular joint axis of the robot can be assumed to perform acceleration / deceleration and constant velocity motion as shown in FIG. 2. As in FIG. 1, in FIG. 2, A represents a starting point, B represents a waypoint, and C represents an end point.

As shown in FIG. 2, the total travel time t _d12 in the AB section (section from the starting point to the _waypoint ) and the total travel time t _d23 in the BC section (section from the waypoint to the _{ending point} ) are It is calculated by the following equations 1a and 1b.

In Equations 1a and 1b, t ₁ is the acceleration time of the AB section (acceleration time at the starting point), t ₁₂ is the constant speed time of the AB section, t ₂ is the acceleration and deceleration time before and after the passing point, and t ₃ is The deceleration time (deceleration time at end point) of BC section is shown, respectively.

Meanwhile, given the moving speed V, the acceleration a, and the moving distance Q, t _d12 and t _d23 may be calculated by the following equations 2a and 2b.

In Equations 2a and 2b, V ₁ is the constant velocity in section AB, V ₂ is the constant velocity in section BC, a ₁ is the acceleration at start point A, a ₃ is the end point in C Acceleration, Q ₁ represents the distance of AB section, and Q ₂ represents the distance of BC section.

On the other hand, since Equations 2a and 2b do not consider the acceleration time at the waypoint B, the actual moving distance is smaller than the given distance.

3 is a graph showing a moving distance not reached when generating an acceleration time before and after the waypoint B. As shown in FIG. As shown in FIG. 3, the actual moving distance does not reach the distance shown by the hatch relative to the given distance.

Hereinafter, a method of calculating the speed and time in each of the start point A, the waypoint B, and the end point C using the above equations will be described.

First, the velocity and time at the starting point are calculated as in Equations 3 to 7 below.

That is, in Equation 2a, V ₁ / a ₁ is equal to the acceleration time t ₁ at the starting point. Thus, when Equation 2a is rearranged using this, the constant velocity V ₁ in the AB section is It is calculated by Equation 3.

Here, t _d12 represents the total travel time in the AB section, Q ₁ represents the distance between the AB sections, and t ₁ represents the acceleration time at the start point.

In order to obtain the acceleration time t ₁ at the starting point, the equations of the constant velocity at the AB section and the velocity at the starting point are summarized, and since they are the same as V ₁ , they can be expressed as Equation 4 below.

After developing Equation 4, the acceleration time t ₁ at the starting point can be obtained by using the formula of Eq.

Here, as described above, a ₁ represents the acceleration at the start point A previously input, and the sign thereof may be determined by the following Equation 6.

Here, SGN means a sign discrimination operator.

On the other hand, the constant velocity time t ₁₂ of the AB section can be calculated by the following equation (7) from the above equation (1a).

Next, the speed and time at the end point C are calculated as in Equations 8 to 12 below.

That is, in Equation 2b, V ₂ / a ₃ is equal to the deceleration time t ₁ at the end point C. Thus, when Equation 2b is rearranged using this, the constant velocity V ₂ in the BC section is It can be expressed as Equation 8 below.

In order to find the deceleration time t ₃ at the end point C, the relational expressions of the constant speed in the BC section and the speed at the end point are summarized, and since they are the same as V ₂ , they can be expressed as Equation 9 below.

After developing Equation 9, the acceleration time t ₃ at the end point can be obtained using the formula of Eq.

Here, as described above, a ₃ represents the acceleration at the end point C previously input, and the sign thereof can be determined by the following equation (11).

Here, SGN means a sign discrimination operator.

On the other hand, the constant velocity time t ₂₃ of the BC section can be calculated by the following equation (12) from the above equation (1b).

Finally, the time at the waypoint B is calculated by the following equation (13).

Here, a ₂ represents the acceleration at the waypoint B input in advance, and the sign thereof may be determined by the following equation (14).

Here, SGN means a sign discrimination operator.

Meanwhile, the time variables t _d12 , t _d23 , t ₁ , t ₁₂ , t ₂ , t ₂₃ , and t ₃ calculated in the above equations are _unnormalized values. Hereinafter, a process of normalizing these time variables and calculating the movement amount for each sampling time using the normalized time variables will be described.

First, the total travel time t _d12 in the AB section and the total travel time t _d23 in the BC section calculated by Equations 2a and 2b are simply obtained by the following Equations 15a and 15b. Can be normalized to an integer multiple of).

In Equations 15a and 15b, t _d12 'and t _d23 ' represent the normalized total travel time in the AB and BC intervals, ROUND represents a rounding operator, and RST represents a sampling time.

Similarly, if the acceleration time t ₁ at the start point, the acceleration and deceleration time t ₂ at the waypoint, and the deceleration time t ₃ at the end point are normalized to an integer multiple of the sampling time RST, respectively, The normalized acceleration and deceleration times t ₁ ′, t ₂ ′, and t ₃ ′ can be represented by Equations 16a to 16c, respectively.

On the other hand, since the total travel time (t _d12 ', t _d23 ') and the acceleration and deceleration time (t ₁ ', t ₂ ', t ₃ ') are normalized as described above, the constant speed time (t ₁₂ ) and BC in the AB section The constant velocity time t ₂₃ in the section may also be normalized using Equations 1a and 1b as in Equations 16d and 16e.

In addition, by using the normalized time variables as described above, each of the changed speeds V ₁ ', V ₂ ' and accelerations a ₁ ', a ₂ ', a ₃ 'can be recalculated by the following equations.

First, the constant velocity V ₁ ′ in the AB section may be calculated using Equation 3 as shown in Equation 17a.

The constant velocity V ₂ ′ in the BC section can be calculated using Equation 8 as shown in Equation 17b below.

Next, the acceleration a ₁ ′ at the starting point A may be calculated using Equation 4 as shown in Equation 18a.

The acceleration a ₃ ′ at the end point C may be calculated using Equation 9 as shown in Equation 18b below.

The reason why the negative sign is given is that a ₃ ′ is the acceleration in the deceleration section.

Meanwhile, the acceleration a ₂ ′ at the waypoint B can be calculated using Equation 13 as shown in Equation 18c below.

Using the time variables calculated by Equations 15a to 18c, the speed and the acceleration, the control unit of the robot calculates the distance, that is, the position data, to move each axis at every sampling time t as follows.

First, the position data Q ₁ (t) in the AB section is sequentially calculated by the following equations 19a to 19c.

That is, as shown in FIG. 2, in the section where t = t ₁ ', Q ₁ (t) is calculated by Equation 19a.

In the section where t = t ₁ '+ t ₁₂ ', Q ₁ (t) is calculated by Equation 19b.

In the section where t = t ₁ '+ t ₁₂ ' + 0.5t ₂ ', Q ₁ (t) is calculated by Equation 19c.

Next, the position data Q ₂ (t) in the BC section is sequentially calculated by the following equations 20a to 20c.

That is, in the section where t = 0.5t ₂ ′, Q ₂ (t) is calculated by Equation 20a.

In a section where t = 0.5t ₂ '+ t ₂₃ ', Q ₂ (t) is calculated by Equation 20b.

In the interval where t = 0.5t ₂ '+ t ₂₃ ' + t ₃ ', Q ₂ (t) is calculated by Equation 20c.

As described above, according to the present invention, the time variables (t _d12 , t _d23 , t ₁ , t ₁₂ , t ₂ , t ₂₃ , t ₃ ) calculated during the velocity profile generation during the continuous motion of the robot are determined. By normalizing to an integer multiple of each sampling time RST, it is possible to prevent a position error from occurring at the end point.

In addition, according to the present invention, since accurate time calculation is possible, a smooth curve of the velocity profile can be easily implemented.

In the above, certain preferred embodiments of the present invention have been illustrated and described. However, the present invention is not limited to the above-described embodiments, and various modifications can be made by those skilled in the art without departing from the gist of the present invention as claimed in the claims. will be.

Claims (4)

(a) calculating time variables of acceleration and deceleration time and constant velocity time based on a given speed, acceleration and moving distance; (b) normalizing the time variables to an integer multiple of the sampling time; And (c) calculating a velocity profile and an acceleration in each movement section using the normalized time variables. The method of claim 1, wherein the normalization of the time variables in step (b) is performed by the following equation; Where t _i 'denotes a normalized time variable, t _i denotes a time variable before normalization, ROUND denotes a rounding operator, and RST denotes a sampling time. The method of claim 2, wherein the speed in step (c) is calculated by the following equation; Where V ₁ 'represents the constant velocity, t _d12 ' represents the normalized total travel time, t ₁ 'represents the normalized acceleration time, and Q ₁ represents the travel distance. 4. The method of claim 3, further comprising calculating a movement amount for every sampling time by using the calculation results in steps (b) and (c).